(Signaling - Sequential Games of Incomplete Information) Consider a firm offering a product that may be either high quality (probability 0.3 ) or low quality (probability 0.7). The firm knows its own type, but the consumer does not. The consumer earns a payoff of 100 from purchasing the high-quality product but 0 from purchasing a low-quality product, and she earns 50 if she doesn't make a purchase. Furthermore, the firm earns a profit of 100 from selling a high-quality product (since it will have gained a loyal customer), 30 from selling a low-quality product (since it will be a onetime sale and the customer avoids purchasing from the firm ever again), and 0 from not making a sale. Prior to the customer making the purchase, the firm can take a costly action: it can pay 80 for a 30-second Super Bowl ad. a) Write the game in extensive form, similarly as we have done it in the job market signaling model in the lecture. b) Find any pooling perfect Bayesian equilibria. c) Is there a separating perfect Bayesian equilibrium in which the high-quality firm advertises and the low-quality firm does not